A New Algorithm for Computing the Determinant and the Inverse of a Pentadiagonal Toeplitz Matrix

DOI: 10.4236/eng.2013.55A004    3,878 Downloads   5,776 Views   Citations
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ABSTRACT

An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.

Cite this paper

Y. Chen, "A New Algorithm for Computing the Determinant and the Inverse of a Pentadiagonal Toeplitz Matrix," Engineering, Vol. 5 No. 5A, 2013, pp. 25-28. doi: 10.4236/eng.2013.55A004.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[2] E. Kilic and M. Ei-Mikkawy, “A Computational Algorithm for Special nth Order Pentadiagonal Toeplitz Determinants,” Applied Mathematics and Computation, Vol. 199, No. 2, 2008, pp. 820-822. doi:10.1016/j.amc.2007.10.022
[3] J. M. McNally, “A Fast Algorithm for Solving Diagonally Dominant Symmetric Pentadiagonal Toeplitz Systems,” Journal of Computational and Applied Mathematics, Vol. 234, No. 4, 2010, pp. 995-1005. doi:10.1016/j.cam.2009.03.001
[4] S. S. Nemani, “A Fast Algorithm for Solving Toeplitz Penta-Diagonal Systems,” Applied Mathematics and Computation, Vol. 215, No. 11, 2010, pp. 3830-3838.
[5] Y. H. Chen and C. Y. Yu, “A New Algorithm for Computing the Inverse and the Determinant of a Hessenbert Matrix,” Applied Mathematics and Computation, Vol. 218, 2011, pp. 4433-4436. doi:10.1016/j.amc.2011.10.022
[6] G. H. Golub and C. F. Van Loan, “Matrix Computations,” 3rd Edition, Johns Hopkings University Press, Baltimore and London, 1996, pp. 193-202.

  
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